Limit-Cycle-Oscillator Models of Bipolar Disorder: Revisited

Years ago, Steve Wirkus and I coauthored (with several undergraduate students) a paper that first introduced the idea of using limit-cycle oscillators to model bipolar patients. Our model was a toy model, but years later several of my colleagues at Oxford have been doing amazing things from a more data-centric perspective. Their latest paper is especially exciting for me. It does what we dreamed about and speculated about 12 years ago in our paper: taking the basic idea of a limit-cycle oscillator and combining it with clinical data in a realistic way. (The authors of this work understandably also incorporate noise into their model.)

Quoting the last few lines of our conclusions: "In this respect, we view our work as a first step in developing mathematical models of the mood swings of bipolar individuals. Our intent is to provide a mathematical framework that ultimately leads to the development of more detailed models of bipolar disorder that incorporate clinical data. With this work, we hope to motivate the collection of time-series data from clinical trials that will lead to refinements of our model that incorporate such data. In our view, dynamical systems theory and mathematical modeling in general can lead to important advancements in the understanding of bipolar disorder."

(Tip of the cap to Society for Industrial and Applied Mathematics, who shared a popular account of the work on Facebook.)

Our Work on Modeling of Bipolar Individuals in The Guardian

The title of the entry basically already says everything, but Marc Abrahams (of Ig Nobel Prizes fame) has written an article about our work on modeling bipolar individuals in The Guardian. An excerpt of the blurb also appears in the Improbable Research blog.

The peanut gallery is skewering us. (Well, there is a mixture of coherent opinions that happen to be different from mine --- which I respect, as one could then have an intelligent discussion with such people about the merits or lack thereof of our research --- and then people who are just either trolling or being vitriolic.) I still need to learn not to read the comments section when one of my articles makes the press. Inevitably, those comments are not going to improve my mood.

In case you were wondering, if you look in the papers that have cited our paper (even though there are not many such papers), you will see that some of our ideas have helped subsequent work, that there is now more scientific evidence that the toy model that we cooked up does seem to capture some things (a similar model has now been derived mechanistically drawing from biochemical considerations), etc. The idea is that one can start with a toy model as a perspective to try to get at the simplest possible mechanisms and use such things --- in combination with clinical data to estimate parameters in such simplistic models --- to really try to get somewhere. This is a complementary way to "Big Data" approaches, and I think that trying to use simple (and even extremely simplistic) models can guide experiments, clinical studies, and so on. Our work on its own cannot do this, as we didn't use real data (which we didn't have), but modelling can inform clinical studies (and experimental studies more generally), and data from such studies can be incorporated into simple models to really try to get somewhere. Our paper is one extremely small stone in this endeavor, but I do believe that it is genuinely a stone.

Ig Nobel Show from Friday

Stevyn Colgan has written a wrap up of the Ig Nobel show two days ago. I was one of the performers. Alas, despite the description, I have not actually won an Ig Nobel prize. :(

If a video shows up later, I'll post it. In the meantime, go to 39:00 in this video of the entire 2012 Ig Nobel show at Imperial College if you want to see me give my 5-minute comedic presentation on cow synchronization.

Mathematical Models of Bipolar Disorder

I've blogged about this paper multiple times before---including discussions of a very snarky letter-to-the-editor that my colleague and I wrote.

The paper itself has now been assigned its official journal volume, number, and page numbers. You can find the article here.


Title: Mathematical Models of Bipolar Disorder

Authors: Darryl Daugherty, Tairi Roque-Urrea, John Urrea-Roque, Jessica Troyer, Stephen Wirkus, and Mason A. Porter

Abstract: We use limit cycle oscillators to model bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes and afflicts about 1% of the United States adult population. We consider two non-linear oscillator models of a single bipolar patient. In both frameworks, we begin with an untreated individual and examine the mathematical
effects and resulting biological consequences of treatment. We also briefly consider the dynamics of interacting bipolar II individuals using weakly-coupled, weakly-damped harmonic oscillators. We discuss how the proposed models can be used as a framework for refined models that incorporate additional biological data. We conclude with a discussion of possible generalizations of our work, as there are several biologically-motivated extensions that can be readily incorporated into the series of models presented here.

Comment on "Bifurcation Analysis of Parametrically Excited Bipolar Disorder Model"

A while back, I blogged about a letter to the editor a collaborator and I wrote regarding a paper that was suspiciously similar to our work. Here is the published version of that letter. Notice the snarkiness at the end. Here is my old blog entry.

By the way, I don't remember if I blogged about this previously, but the ending ended up being a happy one: Because of this whole business, the previously-unpublished article by my collaborators and me (which had been on the arXiv preprint server since 2003) has now been accepted by the very same journal that published the article that raised our ire.

Vintage Mason

Most of you have probably witnessed what I consider to be vintage examples of my sarcastic wit. One MTBI student (Carlos Torres) even came up with the term "Mason moment" to describe verbal instances of such incidents in the context of scientific discussions (such as seminar questions and comments), although those were intended to be pointed but not necessarily sarcastic. (Admittedly, some of those comments have occasionally ended up being less mild than I intended.) Several of you probably have also witnessed the depths that my sarcasm can reach more often than you'd like. :) Here is the latest in a continuing series:

A few months back, one of my collaborators passed a paper on to me that was sent to him by his former Cornell advisor (who is on the editorial board of the journal that published the paper), who I also know pretty well. The reason that paper was brought to my collaborator's attention was that it concerned a nonlinear oscillator model of bipolar disorder, about which we wrote a paper in 2003. We never were actually able to publish this paper (though a few people have cited it anyway and at least a couple of psychologists seemed to be interested in it), but we posted the paper on the arXiv preprint server in 2003.

It turns out to be a very good thing that we posted the paper publicly in a manner that includes a time-stamp, because the article that was forwarded to us had a lot of very familiar ideas, analysis, etc. Once we saw this, we contacted the author to let him know about our paper and asked for his thoughts and to add a reference to it if at all possible. (His paper is already published online, but it's "in press" in the sense that it has not yet been assigned volume, issue, or page numbers.) We waited around a month or so and got no response, so we contacted the editor of the journal and gave him the link to our paper (and indicated the time stamp). To his credit, the journal editor immediately saw a problem and e-mailed the author later that day and asked him to comment on the differences between the two manuscripts. Another month (roughly) passed and the author still hadn't responded, so we asked the editor what we should do. Based on consulting with him, it was agreed that we should write a Letter to the Editor. Perhaps the final version will be edited by the folks at the journal, but here is the way it currently reads. Pay special attention to the last two sentences. As I mentioned, it's vintage Mason.

Anyway, sometimes one has to fight the good fight.

Update: The receipt of our Letter to the Editor was acknowledged at 3:54 pm (pacific time) and it was accepted without comment at 3:55 pm. I'm still waiting for my first negative-time paper acceptance. :)